Almost three times as many people oppose the UK taking part in military action against Syria as those who favour doing so, according to a special Opinium/Observer poll.

The survey straddled the period immediately before and after last Thursday night's House of Commons vote, which saw David Cameron defeated in his attempt to win parliamentary backing for joint UK action against Syria, alongside the US.

The fieldwork was carried out on Wednesday, Thursday and Friday of last week when media coverage of the issue was at its peak.

About 60% of those questioned said that, given the level of evidence about the use of chemical weapons by the Bashar al-Assad regime, they were against British troops intervening, while 24% said they were in favour. Among Conservative supporters 34% were in favour and 50% against, while 24% of Labour backers were in favour and 59% against.

The Liberal Democrats are the most evenly split of the three main parties, with 50% in favour and 36% against. More men (27%) than women (22%) back intervention.

The findings underline the depth of public opposition that Cameron faced last week as he tried in vain to swing parliament behind military action.

When asked what they believed was the main motivation of Cameron in backing action, only 21% said they thought the prime minister acted mainly because he "genuinely believed that in using chemical weapons Syria had crossed a red line and acted badly."

In all, 71% of voters said they felt that recent military actions in Libya, Afghanistan and Iraq had made them less likely to back other UK interventions abroad, with 47% of Tory backers saying they had become a little or a lot less supportive as a result and 17% saying they had become more supportive. Among Labour backers, 58% had been put off against 18% who were more in favour. Among Lib Dems, the poll found 50% were less supportive and 18% more enthusiastic.

Photograph: Opinium

Opinium Research carried out an online survey of 1,942 British adults aged 18+ from 28 to 30 August. Results were weighted to nationally representative criteria